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Dec 15, 2023, 11:39:58 AM12/15/23

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*The philosophical foundation of analytic knowledge*

Analytic knowledge is the set of expressions of formal or natural

language that are connected to the semantic meanings that make them

true.

Thus when we construe provability broadly within the Curry-Howard

isomorphism, we understand that unprovable (within this body of

human knowledge BOHK) simply means untrue.

*I now prove that such a system cannot be incomplete in the Gödel sense*

*There are two mutually exclusive possibilities*

(a) The BOHK can prove every instance of (formal system /expression)

pair that cannot be proved making the BOHK complete.

(b) The BOHK cannot prove some instances of (formal system /expression)

pairs cannot be proved, thus humans have no way to know that they cannot

be proved.

The BOHK cannot possibly be incomplete in the Gödel sense. It is either

complete in the Gödel sense or its incompleteness cannot be shown.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

Analytic knowledge is the set of expressions of formal or natural

language that are connected to the semantic meanings that make them

true.

Thus when we construe provability broadly within the Curry-Howard

isomorphism, we understand that unprovable (within this body of

human knowledge BOHK) simply means untrue.

*I now prove that such a system cannot be incomplete in the Gödel sense*

*There are two mutually exclusive possibilities*

(a) The BOHK can prove every instance of (formal system /expression)

pair that cannot be proved making the BOHK complete.

(b) The BOHK cannot prove some instances of (formal system /expression)

pairs cannot be proved, thus humans have no way to know that they cannot

be proved.

The BOHK cannot possibly be incomplete in the Gödel sense. It is either

complete in the Gödel sense or its incompleteness cannot be shown.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

Dec 15, 2023, 8:05:44 PM12/15/23

to

On 12/15/23 11:39 AM, olcott wrote:

> *The philosophical foundation of analytic knowledge*

>

> Analytic knowledge is the set of expressions of formal or natural

> language that are connected to the semantic meanings that make them

> true.

>

> Thus when we construe provability broadly within the Curry-Howard

> isomorphism, we understand that unprovable (within this body of

> human knowledge BOHK) simply means untrue.

Where does Curry-Howard say unprovable is untrue, my understanding is it
> *The philosophical foundation of analytic knowledge*

>

> Analytic knowledge is the set of expressions of formal or natural

> language that are connected to the semantic meanings that make them

> true.

>

> Thus when we construe provability broadly within the Curry-Howard

> isomorphism, we understand that unprovable (within this body of

> human knowledge BOHK) simply means untrue.

says unprovable is uncomputable/undecidable as it maps computation to

proof, (and says nothing about "true")

>

> *I now prove that such a system cannot be incomplete in the Gödel sense*

> *There are two mutually exclusive possibilities*

>

> (a) The BOHK can prove every instance of (formal system /expression)

> pair that cannot be proved making the BOHK complete.

actually prove anything, it is a collection of "facts".

Thus, you have made a category error.

>

> (b) The BOHK cannot prove some instances of (formal system /expression)

> pairs cannot be proved, thus humans have no way to know that they cannot

> be proved.

unprovable.

The Body of Human Knowledge knows sets of questions that we know one

answer or the other is true, but we have no way of knowing which one is

the true answer, thus it needs to admit the possibility of being incomplete.

>

> The BOHK cannot possibly be incomplete in the Gödel sense. It is either

> complete in the Gödel sense or its incompleteness cannot be shown.

>

Note, systems do not need to "know" they are incomplete to be

incomplete. In fact, in Godel's proof, the system F doesn't know it is

incomplete, its incompleteness is only shown it the meta system derived

from it. You are just showing your lack of understanding of how systems

work.

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